Automating the Math

Automating the Math
Transcribing with MathJax and SRE

University of Birmingham, UK University of Birmingham Crest cs.bham.ac.uk/~vxs

MathJax Consortium MathJax Logo mathjax.org

Progressive Accessiblity Solutions Progressive Access Logo progacc.com

Indian Instiute of Technology, Delhi IITD Logo iitd.ac.in

Background: Initial Problem

Al Maneki reading a tactile math book

Overview

Document formats with math support

Accessibility of these formats

Best option is often to move content to the web

Conversion towards web formats

Keep as much of the source as possible: do not replace the LaTeX

Why is LaTeX important

Creating Tactile Hardcopies

Translate textbooks automatically into Braille from source

What do we do?

What is PreTeXt?

PreTeXt is a an uncomplicated XML vocabulary for open source textbooks, monographs, and research articles.

Aims to bring together the good parts of HTML/Word with LaTeX.

In our context: provides free and well curated content

PreTeXt and Accessibility

What is MathJax?

In our context: translation of LaTeX to Nemeth Braille

Speech Rule Engine

SRE in MathJax

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

Generate Semantics

    ax^2+bx+c=0
<math>
  <mi>a</mi>
  <msup>
    <mi>x</mi>
    <mn>2</mn>
  </msup>
  <mo>+</mo>
  <mi>b</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mi>c</mi>
  <mo>=</mo>
  <mn>0</mn>
</math>

Generate Speech

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

Speech

Play Area for speech

Nemeth in SRE

Sponsored by Big Ten Academic Alliance

Click or focus on the formula and press ENTER to start, Escape to quit.

MathJax on the Server

2D in Nemeth

Quality Assurance

Some Challenging Examples

Nemeth is challenging to get right automatically, but sometimes automation is better:

Voicing Complex Content

$$ \require{bussproofs} \begin{prooftree} \AxiomC{} \RightLabel{$Hyp^{1}$} \UnaryInfC{$P$} \AXC{$P\to Q$} \RL{$\to_E$} \BIC{$Q^2$} \AXC{$Q\to R$} \RL{$\to_E$} \BIC{$R$} \AXC{$Q$} \RL{Rit$^2$} \UIC{$Q$} \RL{$\wedge_I$} \BIC{$Q\wedge R$} \RL{$\to_I^1$} \UIC{$P\to Q\wedge R$} \end{prooftree} $$

Click or focus on the formula and press ENTER to start, Escape to quit.

What about Diagrams?

Some examples from Abstract Algebra

Processing Labels

Processing Labels

Example: Latex to Tactile

Source: Tom Judson, Abstract Algebra: Theory and Application

Cyclic Roots of Unity.

Workflow Example

Unit circle with Braille bounding boxes

Workflow Example

Unit circle with Ascii Braille

Workflow Example

Unit circle with Ascii Braille

Diagrams for Screenreading

circle1group1group4group-2group-3group-4group-6group-7group-8group-9group-10group-11group-12group-13group-40group4group11circlegroup-2group-3group-2group-3group-21group1group-32group1group42circlegroup-6group-7group-8group-9group-10group-11group-12group-13group-4group-6group-7group-8group-9group-10group-11group-12group-13group-61group4group-72group4group-83group4group-94group4group-105group4group-116group4group-127group4group-138group4
Click or focus on the diagram and press A to start, Escape to quit, Escape to quit.

Talking to the Embosser

Example: Poorly embossed

Diagram bad for embosser

Example: Legibly embossed

Diagram bad for embosser

Example: Best solution

Diagram bad for embosser

Some Conclusions